You can swing through the tri-cites Grand Island, Hastings, and Kearney..
Hastings is the "birthplace" of Kool-Aide, and we have Kool-Aide days featuring the largest Kool-Aide stand in the USA plus the hastings Museum and the Leid IMAX theater is pretty cool... Kearney is a really nice town, good shopping and nice places to eat. Grand Island is good for shopping and counting "illegals" of course you are from Cali, so you probably know this game...
Minden Nebraska is home to Pioneer Village which you could take a couple fo days to go through.. really cool museum with lots of pioneer artifacts, plus old cars, etc..
Also on the interstate in Kearney is the Great Platte River Road Monument.. its built over the interstate, and you go through with a headset on, and it has different stations that run through the history of the pioneers and their journey west.. its really neat, and the kids seem to love it.
Really, Nebraska has a TON of really cool attractions.
Toad Stool Park near Crawford, Ft. Robinson where Crazy Horse was killed. That part of the country is rich in history. I grew up about 16 miles SW of Crawford. The Pine Ridge area is very pretty, and there are many other attactions as you wind across Nebraska. Ash Hollow State Park, where the Oregon Trail wagons descended into the North Platte Valley, at Windlass Hill. North Platte, NE, the home to the worlds LARGEST rail road switching yard. Also, home to Buffalo Bill Cody. Stur Museum, and a ton of other attractions await.
I live in Michigan, but grew up in NW Nebraska
Interesting as I grew up in the Gering area of Nebraska and now live in Marshall, MI. I too think the western panhandle section of Nebraska is beautiful and quite different from the eastern 2/3's of the state. The terrain is similar to Wyoming with it's rolling hills. Altitude surprises people as it is mostly 4,000 feet and higher.
I will second Nurmey on the people. I've had the good fortune to live in several states full of really nice people, and Nebraska and Wyoming have to be right at the top of the list of States Absolutely Jam Packed With Nice People.
Besides the people, I'm sure you'll want something to do, as well:
I'll second the Fort Robinson suggestion, it's a great place to visit;
Chimney Rock and the Scotts Bluff National Monument are interesting;
Agate Fossil Beds in Sioux County is fun;
there are some decent lakes for boating/camping/fishing if you're into that (I am);
I'm not as familiar with the eastern part of the state, but I'm sure there are plenty of things to do there, as well;
If you're into learning about where your food comes from, you could learn a lot by just driving through Nebraska and keeping your eyes open.
The Zoo is pretty cool and I have lots of memories of it as a kid... but I am surprised nobody mentioned Cabelas.
Not one, not two, but three Cabela's!
Their World Headquarters is in Sidney, NE.
I've been to many Cabela's all over the US and I own less than $200 worth of their products. I take the family to them because they are incredible. Lots of parking for when we tow trailers, food inside if we get hungry, stuff for the young kids to do as well as us older kids.
When Cabela's put in a store in Michigan, at Dundee, it became the #1 tourist spot in Michigan. More people visit that store than anyplace else in Michigan.
Interesting as I grew up in the Gering area of Nebraska and now live in Marshall, MI. I too think the western panhandle section of Nebraska is beautiful and quite different from the eastern 2/3's of the state. The terrain is similar to Wyoming with it's rolling hills. Altitude surprises people as it is mostly 4,000 feet and higher.
They have a nice little zoo right there in Scottsbluff. I used to live in Gering some years ago when I worked for Lockwood Corp.